Colombia, second in the South American standings, struggled to find a way through a rugged Venezuelan defence at San Cristobal’s Pueblo Nuevo Stadium.
Colombia badly missed the invention of injured talisman James Rodriguez, while captain Radamel Falcao struggled to find the route to goal.
The Colombians had Arsenal goalkeeper David Ospina to thank for a desperate save from Salomon Rondon on 71 minutes as Venezuela enjoyed a rare spell of pressure.
The result sees Colombia remain in second place in the table with 25 points from 15 games.
Both Uruguay and Chile could overtake the Colombians later Thursday with wins in their respective games against Argentina and Paraguay.
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